Blow‐Up in the Critical Quasilinear Keller–Segel System With Indirect Signal Production

ABSTRACT We study the Neumann initial‐boundary value problem for the following quasilinear chemotaxis system with indirect signal production in with . Here , for all . We prove that and decide about the occurrence of blow‐up: namely, it is seen that if then at each appropriately large mass level , there exist radial initial data such that , and that the associated solution blows up either in finite or in infinite time. Especially, if or then the blow‐up can only happen in infinite time.